The advection-dominated accretion flow for the anti-correlation between the X-ray photon index and the X-ray luminosity in neutron star low-mass X-ray binaries

Abstract

Observationally, an anti-correlation between the X-ray photon index $\Gamma$ (obtained by fitting the X-ray spectrum between 0.5 and 10 keV with a single power law) and the X-ray luminosity $L_{0.5-10keV}$, is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of $L_{0.5-10keV}\sim 10^{34}-10^{36}\mathrm{erg}{\mathrm{s}}^{-1}$. In this paper, we explain the observed anti-correlation between $\Gamma$ and $L_{0.5-10keV}$ within the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS. The ADAF model intrinsically predicts an anti-correlation between $\Gamma$ and $L_{0.5-10keV}$. In the ADAF model, there is a key parameter, $f_{\mathrm{th}}$, which describes the fraction of the ADAF energy released at the surface of the NS as thermal emission to be scattered in the ADAF. We test the effect of $f_{\mathrm{th}}$ on the anti-correlation between $\Gamma$ and $L_{0.5-10keV}$. It is found that the value of $f_{\mathrm{th}}$ can significantly affect the anti-correlation between $\Gamma$ and $L_{0.5-10keV}$. Specifically, the anti-correlation between $\Gamma$ and $L_{0.5-10keV}$ becomes flatter with decreasing $f_{\mathrm{th}}$ as taking $f_{\mathrm{th}}=0.1,0.03,0.01,0.005$, $0.003$ and $0$ respectively. By comparing with a sample of non-pulsating NS-LMXBs with well measured $\Gamma$ and $L_{0.5-10keV}$, we find that indeed only a small value of $0.003\lesssim f_{\mathrm{th}}\lesssim 0.1$ is needed to match the observed anti-correlation between $\Gamma$ and $L_{0.5-10keV}$. Finally, we argue that the small value of $f_{\mathrm{th}}\lesssim 0.1$ derived in this paper further confirms our previous conclusion that the radiative efficiency of NSs with an ADAF accretion may not be as high as $\epsilon \sim \frac{\dot{M}GM}{R_{\ast }}/\dot{M}{c}^2\sim 0.2$.

12 pages, 12 figures. Accepted for publication by MNRAS

References in corpus (12)

• Evaluating Spectral Models and the X-ray States of Neutron-Star X-ray Transients
• Correlation between the photon index and X-ray luminosity of black hole X-ray binaries and active galactic nuclei: observations and interpretation
• The hard X-ray spectral evolution in X-ray binaries and its application to constrain the black hole mass of ultraluminous X-ray sources
• Cooling of Accretion-Heated Neutron Stars
• A Hard X-Ray Power-Law Spectral Cutoff in Centaurus X-4
• The Radiative Efficiency of a Radiatively Inefficient Accretion Flow
• The puzzling source IGR J17361-4441 in NGC 6388: a possible planetary tidal disruption event
• X-ray spectral variability of LINERs selected from the Palomar sample
• Constraining black hole masses in low-accreting AGN using X-ray spectra
• Unveiling the nature of compact object in the LMXB MAXI J1957+032 using Swift-XRT
• A systematic study of the advection-dominated accretion flow for the origin of the X-ray emission in weakly magnetized low-level accreting neutron star
• Two-temperature radiative hot accretion flow around neutron stars

Cited by in corpus (1)

• The radiative efficiency of neutron stars at low-level accretion